I don't know the specifics but with some googling, I found this link to an article and read some scientific articles to boot.
Hanging, when carried out with modern techniques, can be one of the quickest and most painless ways to be executed. But not all hangings are designed that way.
health.howstuffworks.com
"The goal of the long drop is to get the body moving quickly enough after the trap door opens to produce between 1,000 and 1,250 foot-pounds of torque on the neck when the noose jerks tight. This distance can be anywhere from 5 to 9 feet (1.5 to 2.7 meters). With the knot of the noose placed at the left side of the subject's neck, under the jaw, the jolt to the neck at the end of the drop is
enough to break or dislocate a neck bone
called the axis, which in turn should sever the person's spinal cord. In some cases, the hangman jerks up on the rope at the precise moment when the drop is ending in order to facilitate the breakage."
This is from The National Library of Medicine:
"The cause of death in judicial hanging is controversial and often attributed to 'hangman's fracture' of the second cervical vertebra. Research has shown that such fractures are the exception in judicial hangings and the cause of death can be attributed to a range of head and neck injuries, particularly compression or rupture of the vertebral and carotid arteries leading to cerebral ischaemia. The rapidity of loss of consciousness and death is highly dependent upon knot positioning and the length of drop which has varied through the history of hanging as a capital punishment in the UK."
It doesn't seem to me like anything with hanging is fool proof.